## Heatmap: Layer vs. Token Correlation ### Overview The image presents a heatmap visualizing the correlation between different layers of a model and specific tokens. The heatmap uses a color gradient to represent correlation values, ranging from approximately 0.5 (light blue) to 1.0 (dark blue). The x-axis represents tokens, and the y-axis represents layers. ### Components/Axes * **X-axis (Horizontal):** Labeled "Token". The tokens are: "last\_q", "first\_answer", "second\_answer", "exact\_answer\_before\_first", "exact\_answer\_first", "exact\_answer\_last", "-8", "-7", "-6", "-5", "-4", "-3", "-2", "-1". * **Y-axis (Vertical):** Labeled "Layer". The layers range from 0 to 30, with increments of 2. * **Color Scale (Right):** Represents the correlation value. The scale ranges from 0.5 (lightest blue) to 1.0 (darkest blue). Intermediate values are marked as 0.6, 0.7, 0.8, and 0.9. * **Legend:** Located on the right side of the heatmap, providing the color-to-value mapping. ### Detailed Analysis The heatmap shows varying correlation strengths between layers and tokens. Here's a breakdown of observed values, noting approximate values due to the visual nature of the data: * **"last\_q" Token:** Shows a generally low correlation across all layers, with values mostly around 0.5 - 0.6. * **"first\_answer" Token:** Exhibits a moderate correlation, peaking around layer 2 at approximately 0.8. Correlation decreases with increasing layer number. * **"second\_answer" Token:** Similar to "first\_answer", with a peak correlation around layer 2, approximately 0.8, and decreasing correlation at higher layers. * **"exact\_answer\_before\_first" Token:** Shows a moderate correlation, peaking around layer 6 at approximately 0.8. * **"exact\_answer\_first" Token:** Displays a very strong correlation, particularly between layers 4 and 10, with values consistently around 0.9 - 1.0. This is the most prominent feature of the heatmap. * **"exact\_answer\_last" Token:** Shows a moderate correlation, peaking around layer 10 at approximately 0.8. * **Tokens "-8" to "-1":** These tokens exhibit a generally increasing correlation with increasing layer number, peaking around layers 24-28, with values around 0.7-0.8. **Specific Data Points (Approximate):** * Layer 0, "first\_answer": ~0.6 * Layer 2, "first\_answer": ~0.8 * Layer 4, "exact\_answer\_first": ~0.95 * Layer 8, "exact\_answer\_first": ~1.0 * Layer 10, "exact\_answer\_first": ~0.95 * Layer 24, "-8": ~0.7 * Layer 28, "-1": ~0.8 * Layer 30, "last\_q": ~0.55 ### Key Observations * The "exact\_answer\_first" token demonstrates the strongest and most consistent correlation with layers 4-10, indicating a strong relationship between these layers and the first exact answer. * The tokens "-8" to "-1" show an increasing correlation with layers, suggesting their importance grows in deeper layers of the model. * "last\_q" consistently exhibits the lowest correlation across all layers. * The correlation for "first\_answer" and "second\_answer" is highest in the earlier layers and decreases as the layer number increases. ### Interpretation This heatmap likely represents the attention weights or activation patterns within a neural network model, specifically related to question answering. The strong correlation between layers 4-10 and the "exact\_answer\_first" token suggests that these layers are crucial for identifying and processing the first exact answer to a given question. The decreasing correlation of "first\_answer" and "second\_answer" with increasing layers could indicate that the initial answer processing is more prominent in the earlier layers, while later layers focus on refining or contextualizing the answer. The increasing correlation of the negative numbered tokens with deeper layers suggests these tokens become more relevant as the model processes information more abstractly. The low correlation of "last\_q" might indicate that the initial question representation is less important for the final answer generation compared to the answer-related tokens. This visualization provides insights into which layers are most sensitive to specific tokens and how information flows through the model during the question-answering process.